It seems to have everything I need. (My interest was in knowing a) whether gravity in general requires multi-light speed of propagation (it does only for Newtonian gravity, and, I guess, any mechanical form of gravity, such as "push gravity"), and b) how general relativity got around this (by the use of velocity-dependent terms).

Now I just need to read and be able to make sense out of Carlip's article, and understand what is meant by "the quadrupole nature of gravitational radiation."

If the intent is to ask what General relativity has to say about the speed of gravity, the answer is fairly clear - it travels at 'c'. This is a prediction of GR, not yet an experimentally established fact.

If the question is more general, it may belong in some other forum, as robphy has perhaps suggested - though I'm not sure exactly which one.

I belive that Van Flandern has actually been published, so that while his ideas may be full of errors and far away from the mainstream, they are probably "fair game" according to PF guidelines (to discuss only published papers, not personal theories).

Good question Jennifer!
In Maxwell's theory of EM waves these propagate in vacuum at "speed" determined by two constants,vacuum permeability and permitivity namely.
Why the speed of propagating of a gravity wave,which at first glance has nothing to do with electrical charges,has to be linked with these two electrical constants, in the same manner?

I should probably add that the speed of gravity is predicted to be equal to 'c' only for weak fields in a vacuum.

When you linearize the Einstein field equations around a vacuum solution, you come up with a set of linear differential equations. The solution to these linearized equations is a plane wave, just as it is in the case of Maxwell's equations. This plane wave travels at a speed of 1 in geometric units, i.e. it travels at the speed of light, since c=1 in geometric units.

I should probably add that the speed of gravity is predicted to be equal to 'c' only for weak fields in a vacuum.

When you linearize the Einstein field equations around a vacuum solution, you come up with a set of linear differential equations. The solution to these linearized equations is a plane wave, just as it is in the case of Maxwell's equations. This plane wave travels at a speed of 1 in geometric units, i.e. it travels at the speed of light, since c=1 in geometric units.

Pervect - can you clarify - are you saying that a plane wave arises from the sudden destruction of matter (conversion to another form such as photons) which is other than gravitational radiation.

. This plane wave travels at a speed of 1 in geometric units, i.e. it travels at the speed of light, since c=1 in geometric units.

Only becouse STR is taken as guide in linearization where c=1.
But this fact about EM was found both experimentally,and theoretically.
The claim that gravity wave propagate with c,isn't found experimentally or theoretically...

Only becouse STR is taken as guide in linearization where c=1.
But this fact about EM was found both experimentally,and theoretically.
The claim that gravity wave propagate with c,isn't found experimentally or theoretically...

This is incorrect. As I explained earlier, it's a standard textbook exercise to derive the theoretical prediction of the speed of propagation of gravitational waves in GR.

As I re-read your remark, I suppose I should add that GR does presuppose SR is true - it doesn't make any sense to postulate GR without also including SR as a special case.

The result is that according to GR, the speed is equal to 'c'. Just about any GR textbook will go into this, see for instance chapter 18 of MTW's "Gravitation". But if you don't happen to have that textbook handy, pick ANY textbook that covers the topic of gravitational waves.

Certain other assumptions are made to make this derivation. One assumes that one has a metric n_uv which satisfies Einstein's field equations. G_uv can be written as a compiclated second-order non-linear differential equation of n_uv. It is simplest and usually assumed that n_uv is a Minkowski metric, so that the background space-time is not only a vacuum solution, but it is flat. This is for ease of computation (and ease of interpretation) though, it's perfectly possible (though trickier) to talk about the speed of gravity in a a Schwarzschild vacuum as well as a Minkowski vacuum.

One then assumes a pertubation metric g_uv = n_uv + h_uv, where h_uv is "small". One then linearizes Einstein's field equations, getting LINEAR second order differential equations in terms of the pertubations to the metric h_uv. These equations are found to be the wave equations, and represent gravitational waves. These waves travel at 'c', the speed of light.

While it is incorrect, as I have attempted to explain at length, to say that there is no theoretical foundation for the speed of gravity being c -according to GR (which is I might add, the title of this forum, i.e. this is a GR forum), it is basically correct to say that we currently have no experimental measurements of the speed of gravity. Here we have a few authors such as Kopeikin arguing that they have performed experiments which indirectly measure the speed of gravity and other authors arguing that since one needs to assume some theory other than GR even to talk about the speed of gravity not being c, that the above measurements which assume GR is true in order to interpret the results as a 'speed' have assumed their conclusion rather than actually measuring the speed. I agree with Carlip on this point, and while Kopekin continues to defend his position I don't think he currently has a lot of support (this is a judgement call).

Pervect - can you clarify - are you saying that a plane wave arises from the sudden destruction of matter (conversion to another form such as photons) which is other than gravitational radiation.

Analyzing the source of gravitational waves is actually a bit different from the simpler task of determining how fast they move. Conversion of matter to energy is not really the central issue behind creating gravitational waves. A spinning assymetrical bar or plate will, for instance, generate gravitational waves without any such conversion. What's important turns out to be the third time derivative of the quadropole moment of the matter distribution. I'm sorry if that's too technical, I'm not sure how to describe it more simply and still be exact.

But it's basically true that the in order to measure the speed of gravity by accepted defitnions, one wants to create a disturbance "here" and then detect the effects "there", and then compute the propagation speed. So, for instance, while the decay of the orbits of the spinning pulsars (Taylor & Hulse) has provided us with indirect evidence that gravitational waves exist (for which they won the Nobel prize), this smooth decay process doesn't really offer us any "handles" on a way to measure the actual speed of gravitational radiation.

One of the ways that I envision the speed of gravity being measured at some point in the future is for us to observe an binary inspiral or other catastrophic event which emits gravity waves both visually and with gravitational wave detectors such as Ligo, assuming they come on-line and work as expected. This is the sort of experiment that will give us the best information about the "speed of gravity" IMO.

It doesn't appear to be technologically possible in the forseable future to create artiically a gravitational wave disturbance that we can detect, therfore we will have to wait for a catastrophic astrophysical event to occur and measure the waves from it.

Currently, though we've built gravitational wave receivers, they aren't very sensitive, and they have yet to detect any signal at all, much less provide timing information about how fast the signal travels. The former issue (detection of signals) is still expected to change as we improve the sensitivity of the receivers - the lack of detection is not considered to be alarming considering the expected frequency and magnitude of natural sources of gravitational radiation.

Certain assumptions are made to make this derivation. One assumes that one has a metric n_uv which satisfies Einstein's field equations. G_uv can be written as a compiclated second-order non-linear differential equation of n_uv. It is simplest and usually assumed that n_uv is a Minkowski metric

So there you go...And what constant,if not "electromagnetic" c ,is fixed in a Minkowski metric?:tongue:

Pervect - so the plane wave you were referring to in post 11 is the quadrapole gravitational radiation. Thanks

One more question with regard to your post 15 - if we assume for example a catastrophic event - say electrons combining with positrons to extinquish matter and release photons (a visual event).. is not the total energy of the original particles accounted for in the radiating photon flux - and if so - where is the energy that is conveyed by the gravitational radiation come from?

It sounds like we might actually agree if you would restrain what appears to be some anti-relativity sentiment. At least that's the way it's coming across to me.

Impression from the books that "electromagnetic" c sets the "gravitational" c.
Quite comfortably,I would rather say that it's the other way round .
However,I don't think this could be the correct standpoint either.c must be the universal constant,not exclusively reserved for electromagnetism or gravity.
Beside the fact that it doesn't deal with the gravity,Maxwell's theory cannot be considered as the complete theory.
Covariance:Maxwel's eqs. for empty space stay unchanged if we apply to space-time coordinates linear tranformations->Lorentz transforms.Covariance holds for a transformation composed of more such transformations.Mathematically that's the property of a Lorentz group.Accordingly,from Maxwell's eqs. arise the Lorentz group,but Maxwell's eqs. from the Lorentz group don't arise .The group can be defined independently of these eqs. as the group of linear transforms with c=1 kept constant.
In GR things are even more interesting ,nonlinear transformations must be applied,and Lorentz group aren't generally valid .
But the point is :in electromagnetism where charges oscillates,we find c. In the gravity,where masses oscillate,we will probably verify one day the same velocity c of the field disturbance propagation.
Also the curiosity :A propagating EM wave induces a gravitational field,but a propagating gravitational wave does not induce a magnetic field.

Impression from the books that "electromagnetic" c sets the "gravitational" c.
Quite comfortably,I would rather say that it's the other way round .
However,I don't think this could be the correct standpoint either.c must be the universal constant,not exclusively reserved for electromagnetism or gravity.
Beside the fact that it doesn't deal with the gravity,Maxwell's theory cannot be considered as the complete theory.
Covariance:Maxwel's eqs. for empty space stay unchanged if we apply to space-time coordinates linear tranformations->Lorentz transforms.Covariance holds for a transformation composed of more such transformations.Mathematically that's the property of a Lorentz group.Accordingly,from Maxwell's eqs. arise the Lorentz group,but Maxwell's eqs. from the Lorentz group don't arise .The group can be defined independently of these eqs. as the group of linear transforms with c=1 kept constant.
In GR things are even more interesting ,nonlinear transformations must be applied,and Lorentz group aren't generally valid .
But the point is :in electromagnetism where charges oscillates,we find c. In the gravity,where masses oscillate,we will probably verify one day the same velocity c of the field disturbance propagation.
Also the curiosity :A propagating EM wave induces a gravitational field,but a propagating gravitational wave does not induce a magnetic field.

I'm still not following you - and I have to run.

Basically, though, the point is that one doesn't know what the speed of gravity (I should perhaps say the speed of gravitational radiation) is just by inspecting the Minkowski line element. One actually have to solve Einstein's field equations. When one does so, using the method I sketched earlier, one finds that the speed of gravitational radiation in a vacuum is 'c'. This is a mathematical result, very similar to the way that Maxwell's equations show that the speed of light is equal to 'c' in a vacuum.

Someone has emailed me that I should be more precise on this point, and I will attempt to do so. When I say that the speed of gravitational radiation is 'c', I don't mean the coordinate speed of gravitational radiation is equal to 'c'. That would be rather silly, for the coordinate speed of light is not always equal to c in GR as GR allows arbitrary coordinate systems. What I mean is that the local speed of gravitational radiation, like the local speed of light is equal to 'c'.